July ,5, 1959
CONFORMATIONS AND STRAIN ENERGY OF CYCLOPENTANE
[COUrRIBUTIOS FROM THE
DEPARTMENT O F CHEMISTRY,
3213
v K I V E R S I T P O F CALIFORNIA, BERKELEY]
Conformations and Strain Energy of Cyclopentane and its Derivatives BY KENNETH S. PITZER AND WILME. DONATH RECEIVEDJANUARY 2, 1959 Earlier calculations of the conformation and strain energy of cyclopentane are refined by the addition of terms for the election correlation energy of non-bonded but nearby atoms and for the zero point vibrational energy The agreement with observed properties of cyclopentane is substantially improved. It is shown t h a t substitution of the cyclopentane will ordinarily yield a harrier t o the pseudo-rotation of ring puckering and t h a t the energy minimum will in some cases correspond t o C 2 symtnetry and in other cases t o Cs symmetry. It is shown t h a t certain of the parameters evaluated for cyclopentane may be transferred to derivatives and t h a t strain energies may becalculated for the derivatives if potential barrier values are available for t h e appropriate open chain model compounds.
In 1941 Aston, Schumann, Fink and Doty' terms do not yield any explanation of the difference showed that the cyclopentane ring was puckered. in energy between such paraffin isomers as nThe torsional forces associated with the single C-C butane and isobutane or n-pentane and neopenbmds are undoubtedly responsible for this pucker- tane. Consequently the lack of quantitative agreeing and semi-quantitative calculations of the ment for the strain energy of cyclopentane was not strain energy and of the detailed equilibrium con- too surprising. Recently calculations for the paraffins were itnformation have been p r e ~ e n t e d . ~ -While ~ the quantitative comparison of these results with the provedl0 by the addition of terms for the zero point experimental heat of combustion value5 was only vibration energy and for the interaction energy of partially satisfactory, a significant qualitative nearby but non-bonded electron clouds. The result emerged from the Kilpatrick, Pitzer and correlation of the motion of these electrons yields Spitzer3 investigations, namely, "that the pucker- an attractive force and an energy decrease which ing of the ring is not of a definite type but that the may be treated by the method used by F. London angle of maximum puckering rotates around the for attractive van der Waals forces between nonring." While certain have been re- polar molecules. These calculations for the parafluctant to accept this pseudo-rotation of the puck- fin isomerization energies yielded quite good agreeering and the consequent indefiniteness of the cy- ment and we now extend the same method to clopentane conformation, McCulloughg has re- cyclopentane and cyclohexane. The numerical constants of previous investigaported more precise heat capacity measurements ? ' ~ London or correlafor cyclopentane which definitely confirm the free tions were r e t a i ~ ~ e d . ~The pseudo-rotation. tion energy is given by the formula It is the purpose of this paper to present: first, 8.682&3-' f new and improved calculations of the total strain A& = - [ 2 2 . 6 2 R ~ c - ~ 3.42ZL?"-6] x lod6' ergs (1) energy of cyclopentane and of the equilibrium degree of puckering, and second, a discussion of the where the sums are over all non-bonded interexpected equilibrium conformation of cyclopentane atomic distances of the types indicated. Boqd derivatives where, in general, the substitution will distances are taken as C-C, 1.54 A.; C-H, 1.10 A. introduce a potential barrier restricting the pseudo- The C-C-C bending constant was taken as 0.8 X rotation. 1O-I' erg/radian2 and the torsional potential Strain Energy of Cyc1opentane.-Previous barrier as a cosine function of 2800 cal./mole height. The puckering in cyclopentane is described by the strain energy calculations for cyclopentane considered only the torsional energy associated with the formula rotation of C-C single bonds and the strain of bending C-C-C bond angles below the tetrahedral value. The force constant for the latter effect was taken from the normal vibration analysis of cyclo- where Zj is the displacement of the jthatom perhexane and open chain hydrocarbons, while the pendicular to the plane of the unpuckered ring, q torsional potential was estimated from that of measures the amplitude, and the phase angle of ethane and other simple hydrocarbons. These two the puckering. The calculations follow the method of Kil( I ) J. G . Aston, S C. Schumann, H. L. Fink and P. M. Doty, ' h i s JOL-KNII., 63, 2D29 (1941), J G .4ston, H. I,, Fink and S C patrick, et ~ 1 . additional ~ ; details are given in the S-humann, ibid , 6 5 , :341 ( 1 9 4 3 ) . Appendix. The results for cyclopentane are given . Spitzer, THISJ O U R N A L , in Table I for six values of the parameter p. The bond energies, C-H, 102.4 and C-C, 80.2 kcal./ 6 9 , 2483 ( 1 9 4 7 ) . (1) R. Spitzer and H XI. Huffman, ibid.,69, 211 (1947). mole, which were obtained in the corresponding ( 5 ) F. D Rossini, e t e l . , "Selected Values of Physical a n d Thermotreatment of the paraffins, together with the disdynamic Properties of Hydrocarbons and Related Compounds," sociation energies of the elements yield the term Carnegie Press, Pittsburgh (1953 and subsequent supplements) - A H b o n d = 59.0 kcal./rnole. The zero point vibra( 8 ) F. A . Miller and R . G.Inskeep, J . Chem. P h y s . , 1 8 , 1619 (1960) ' 7 ) C G LeFevre and R . J \V. LeFevre, J . Chem. .Soc., 3549 (lY5G); tional energy was calculated from the assignment Chemislvy a n d Iniiirstvy, 54 (1Y50) of Miller and Inskeep.6 (8) B. Curnutte and \V. F. Shaffer, J . M o l . Spectvoecop;., 1, 230 A plot (Fig. 1) of the heat of formation -All," (IY57).
+
(0) J. P. RlcCullough, J . C ~ P I IJ 'Ih. y s . , 29, 8 C G (19.58).
(10) K S. Pitzer and E. Catalano, THISJ O T J R N A I . , 78, 4844 11950).
:E14
KENNETH S. PITZER A N D WILME. DONATH
VOl. 51
thus in practical agreement with experiments and with the earlier c a l c ~ l a t i o n . ~ The second derivative of the energy with respect .7, A. 0.00 0.23C 0.308 0.40 0.50 0.60 to q gives the restoring force for the vibration (283 - E c ,kcal./mole 44.49 4-$ 57 41.U7 44.94 45.72 47.03 14.00 1 1 . 4 8 ?I 9Y 8.05 6.18 4.95 Et,,,ian,kcal./mole cm. --l) in which the amplitude of puckering varies. Ec-c-c, k c a l / m o l e 0.08 0 (2 1 10 2.19 4.26 7.52 The effective mass for this vibration was calculated - A t I b o u d , kca1.i only approximately and interaction with other mule 59.0 59 0 59.0 59.0 59.0 59.0 85 26 85.26 85.26 8 5 . 2 6 B ~ / & v kcal./mole , 85.20 8 5 . 2 0 vibrations was neglected. The resulting spectro7.3 8.4 9.0 8.1 -AIIf*,kcal./mole 4.2 (j.2 scopic force constant, k = 1.3 X lo6 dynes/cm., agrees as well as could be expected with that obLIS.y yields a minimum of 9.0 kcal./mole a t 0.50 k. tained from the plot of the values of Table I, These values may be compared with the experi- ca. 1.1 x 105. mental - AoHf' = 10.7 kcal./mole5 and the value of While the 1.7 kcal./mole difference in AHf' 40 = 0.47 A. which fits the experimental entropy." indicates that some further improvement in the The agreement for 40 is excellent and for A H r o theory of the energy is needed, the present results reasonably satisfactory but not within experi- are qualitatively correct in all respects and yield inental error. as close a quantitative agreement as can be expected for a relatively simple theory. A similar calculation for cyclohexane, where there is no torsional or C-C-C angle strain, yields -AHfo = 19.5 kcal./mole at O'K. in excellent agreement with the experimental value of 20.0 kcal./mole. I n this calculation the zero point energy was obtained from the frequency assignment of Beckett, et a1.12 Cyclopentane Derivatives and Related Fivemembered Ring Compounds.-If cyclopentane is substituted in such a manner as to change significantly one or more of the torsional potential barriers, then the cancellation of forces that yield the free pseudo-rotation will no longer be as exact and a potential restricting the pseudorotation is to be expected. An example is thiacyclopentane where Hubbard, et aZ.,I3 found a potential barrier of 2500 cal./mole from their interpretation of spectroscopic and thermodynamic data. An exact calculation of the potential barrier for 01 0 2 0 3 0 4 05 06 7: the pseudo-rotation would require the readjust4. ment of the puckering to minimize the energy for Fig 1 -The calculated heat of formation (in kcal./mole) of cyclopentane as a function of the amplitude of puckering each phase angle between the puckering maximum and the substituted atom. However, we may obq in A tain approximate results by assuming that the bond The calculations reported in Table I were made twist angles remain the same as in cyclopentane for cyclopentane in the conformation of CS sym- itself. These are shown for the two symmetrical in Fig. 2 and Table I1 for PO = metry, ;.e., with 'p = 0 or any integral multiple conf~t;mations'~ of ~ / 1 0in equation 2. The various terms mere also 0.48 A. The extreme difference in energy for a calculated for the C? conformation which may be single substitution is obtained by placing the subobtained on substitution of any odd integral stituent in the unique position in each case (posimultiple of n / 2 0 for cp. The simplest case is tion one in Fig. 1). There are, of course, interp = - 3n/20 which yields z 1 = 0 and thus places atom TABLE I1 one on the nsyninietry axis. A near equilibrium TORSTONAL ANGLES I N CYCLOPENTANE value 0.48 ,4. was taken for y and the following CS CI values were obtained: - E c = 45.0, E t o r s i o n = 012 = 051 46.1' 15.15' 6.5, Ec-c-c = 3.77, -AHfo = 8.5 kcal./mole. 023 = B45 28.6' 39,450 The torsional and bond bending strain energies are 0.O0 48.1O 054 very close to the comparable values for q = 0.48 1 + COS 3el2 0.25 1.70 interpolated from Table I. The electron correla1 + COS 3eZ3 1.07 0.52 tion energy and the net heat of formation differ by cos 3034) 1 00 0 09 1!2(1 about one-half kilocalorie from the values for the C S form; we are not sure whether this difference is (12) C . W. Beckett, K. S. Pitzer and R. Spitzer, ibid., 69, 2488 significant or not (see -4ppendix). It may be con- (1947). (13) W. N. Hubbard, H. L. Finke, D. W. Scott, J. P. McCullough, cluded, nevertheless, that the calculated energy C. Katz, M. E. Gross, J. F. Messerly, R. E. Pennington and G U Y difference between C? and CS forms is small and Waddington, ibid., 74, 6025 (1952). TABLE I ENERGY OF CYCLOPENTANE AT OOK.
-lob
+
(11) T h e original calculation of Kilpatrick, Pitzer a n d SpitzerS used an erroneous symmetry number of 5 instead of 10. Correction of this error doubles the value of qo. See THISJOURNAL, 80, 6697 (1958).
(14) T h e names envelope a n d half chair have been suggested for t h e Cg and CP farms, respectively, b y Brutcher (private communication). These terms seem t o t h e writer to be appropriate if descriptive names are desired in addition t o the symmetry symbols.
July 5, 1959
mediate conformations between CZ and CS which have the same energy in cyclopentane and smoothly varying energy in substituted molecules. Also conformations obtained by placing the substituent in an unsymmetrical position in the CZand CSforms are also real but of intermediate energy. The last three lines in Table I1 give the coefficients of the potential barriers VlZ = V ~ I ,V7!3 = 54'L and V34, respectively, in the torsional strain energy. If we wish only the energy difference AVc for the conformation change Cs --+ Cz, we obtain AVC
0
CONFORi'dATIONS AND STRAIN
1.45Vi1
- 0.55V~a- 0.91Vai34
(3)
This torsional energy difference may be taken as a good approximation to the net difference in total energy unless some special complication such as a repulsive steric hindrance is present. If all potential barriers are the same, the result is zero within computational error as stated above. Let us now consider in particular the case where substitution has occurred a t position one in cyclopentane. The barriers are 2800 cal./mole except for VIZ = which may be different. Then
ENERGY OF CYCLOPENTANE
3215 I
I
5
5
4 .IO
.IO
I
I
3
f
i
4 -29
I
29 3
I
cs c2 Fig. 2.-The two symmetrical conformations of cyclopentane. Figures inside the circles show equilipiurn displacements perpendicular to plane of the paper in A . ; figures outside the circles indicate the numbering adopted for the carbon atoms.
The model compounds chosen for obtaining V12 values are given in the footnotes to Table 111. It should be remembered that the essential quantity is the difference in the potential barrier of the model compound from that of ethane. Also we wish to AVO = 1.45( Vl2 - 2800) cal./mole (4) where the change is CS CZ as before. Table avoid possible steric repulsions between the hydroI11 contains values of 1 / 1 2 taken from appropriate gen atoms of methyl groups which arise in commodel molecules and the resulting AVc values for pounds such as dimethyl ether but which do not several substituted cyclopentanes and related arise in the corresponding ring, in this case tetracompounds containing saturated five-membered hydrofuran. The approximation of taking cyclopentane bond rings. torsional angles for these other substances will It should be emphasized that the AVc values in Table I11 are potential barriers to the pseudo- tend to make the calculated AVc values too large. rotation which is restricted in these cases. A posi- Consider, for example, cyclopentanone with its tive value of AVc indicates that the lowest energy small VI*. The assumed model for the stable C2 phase angle of puckering is the symmetrical CS form will be nearly correct because the reduction form; a negative value indicates that the lowest of V12 from cyclopentane to cyclopentanone will energy phase angle is the symmetrical CZ form. tend only to reduce el2 which is already small. One may assume that a simple cosine function However, in the high energy Cs form 812 is larger yields a good approximation for the energy of all than optimum for the low V I , of cyclopentanone. intermediate values of the phase angle. Thus Reduction in the puckering parameter reduces the AVc is not the energy difference between separate C-C-C angle strain a t moderate cost in torsional potential minima such as the equatorial and axial strain. A quantitative calculation for the CS conformations of methylcyclohexane but is the form of cyclopentanone (assuming still the E c height of the energy barrier restricting the rotation values of cyclopentane) indicates that the corrected potential is only 0.2 kcal./mole lower (at a of the phase of puckering. value of 4 0 about 0.04 A. smaller) than was obtained on the approximate basis of Table 111. TABLE I11 Thus this effect is small and may be ignored in apPOTENTIAL BARRIERSTO PSEUDO-ROTATION IN CYCLOPENproximate calculations. TANE DERIVATIVES The calculated value of AVc in Table 111 for Substance VI2 A Vc thiacyclopentane of -3.0 kcal./mole is in good Meth ylc yclopentane 3.40" 0.9 agreement with the experimental value 2.8 Fluorocyclopentane 3. 30b O.i kcal./mole obtained by Hubbard, et al.I3 The 1.98" -1.2 Methylenecyclopentnne thermodynamic method used in their work deCyclopentanone 1.15d -2.4 termines the magnitude but not the sign of the 1 90" -1.3 Pyrrolidine potential barrier. McCulloughg reports that the Tetrahydrofuran 1 Oi' -2.5 value for pyrrolidine is small without indicating Thiacyclopentane 0.71' -3 0 an upper limit. The calculated value of -1.3 a Propane: IC. S. Pitzer, J . Chem. Phys., 12, 310 (1944). kcal./mole is certainly much smaller than that for " E t h y l fluoride: D. Herschbach, ibid., 25, 358 (1956). thiacyclopentane and may be small enough to Propylene: D. I t . Lide, Jr., and D. E. Mann, ibid., 27, 868 (1957). Acetaldehyde: R. W. Kilb, C. C. Lin and yield agreement with experiment.
-
E. B. Wilson, Jr., ibid., 26, 1695 (1957). a Methylamine: D. R. Lide, Jr., ibid., 22, 1613 (1954); Shimoda, Nishikawa and Itoh, J . Phys. SOC.Japan. 9, 947 (1954). 'Methanol: E. V. Ivash and D . M . Dennison, J . Clzem. Phys., 21, 1804 (195.7); J . D. Swalen, ibid., 23, 1739 (1955). 0 Methanethiol: R. W. Kilb, zbid., 23, 1736 (1955).
Discussion The data presented in Tables I1 and 111 provide the basis for estimates of strain energies for many five-membered ring systems. For maximum ac-
KENNETH S. PITZER AND WILME. DONATH
3216
curacy one should readjust all of the molecular parameters in order to minimize the strain energy for each individual case. A few exploratory calculations indicated, however, that useful estimates of strain energy differences may be obtained in many cases by retaining the geometry of cyclopentane but recognizing the difference in torsional potential barriers caused by the substitution. In making such calculations it is essential to select the conformation of cyclopentane which will be most stable in the substituted molecule. Thus a single substituent which raises the two adjacent barriers (Vi2 = VSI)stabilizes the symmetrical Cs form whereas if a single substituent lowers the adjacent barriers the symmetrical CZform becomes the most stable. One may then calculate torsional strain energy differences by multiplying the appropriate value of (1 cos 3OlZ)in Table I1 by the difference in potential barrier height VlP. If two molecules are to be compared which have different stable
+
. .
.
methyl group in the most axial conformation The absence of steric repiilsiuns analogous to aria1 methylcyclohexane is apparent.
Vol. 81
conformations, then one must compare each with cyclopentane and sum the two differences. A case of this type will be illustrated below. The possibility. of steric repulsions analogous to those of axial substituents in cyclohexane must also be considered. Examination of appropriate models (Fig. 3) shows no large interference in the cyclopentane case for the methyl group or any smaller group. An approximate quantitative value for the axial-equatorial energy difference can he obtained from the heat of formation valuess found for cis- and trans-l,3-dimethylcyclohexaneswhich are -22.19 and -21.65 kcal./mole, respectively, a t 0%. The cis isomer has a di-equatorial conformation while the trans is axial-equatorial. Hence the energy difference of 0.54 kcal./mole may be ascribed to the extra strain of the axial methyl group. The corresponding value for the cyclohexane system is. of course. much lamer (ca. . 1.9 kcal./mole). ' The terms axial and eauatorial are descrbtive only for that portion of thecyclopentane ring where the C-C bonds are in a nearly staggered orientation. We see from Table I1 that the 1,2- and 5,lbonds in the Cs form are nearly staggered, hence the three successive positions 5, 1 and 2 qualify. In 1,3-dimethylcyclopentanesthe methyl groups would be expected to be in positions 5 and 2 of the Table I1 numbering for the C8 form. Since the e a energy difference is small, the value AVc = 0.9 kcal./mole in Table 111 for methylcyclopentane may be interpreted as a good approximation to the net barrier to pseudo-rotation in that molecule. This agrees well with the value selected by Kilpatrick, etal.," 0.75 kcal./mole which is consistent with the entropy of methylcyclopentaue.' Conversely one may regard the agreement just cited as confirming the low e a energy difference in methylcyclopentane. Cases of axial conformation of groups larger than methyl or of conformations which are di-axial on the same side of the ring may have large strain but need individual consideration. Let us now consider particular data of several types which relate to the strain of saturated fivemembered rings. The heats of hydrogenation measured by Turner and Garner'% for methylenecyclopentane (-26.9 kcal./mole) and methylenecyclohexane (-27.8 kcal./mole) may be interpreted to yield the difference in strain energy of methylcyclopentane and methylenecyclopentane. If all thermal energy terms are assumed to cancel and both cyclohexane compounds are strain free,'& then one assigns the difference of 0.9 kcal./mole to an increased amount of strain in methylcyclopentane over that in methylenecyclopentane. (15) J. E.Kilpatrick, H. G. W-er, C. W.Beckett. K.S. Pitrerand F. D. Rossioi, . I Research . N o l l . Bur. Slondordr. $9. 523 (1947). (16) R. B. Turner and R. H.Gamer. TU15 l0uanA.L 79, 253 (1957); 80, 1424 (1958). (16a) H.C . Brown, J. H. Brewstter. and H. Shechter, TRIS Jouan&L. 16, 467 (1954). assume that the introduction 01 an e m double bond into cyclohexane introduces strain. T h e structural explanation Dropoaed was rtrain associated with the opposed orientation of the double bond relative to the C-H bonds of adjacent ring methylene groups. Recent microwave Studies (ref. d of Table I l l and D. R. Herschbaeh and L. C. Krisher, J . Chcm. Phy,., 98, 728 (1958)) have shown that this opposed orientation is the etable orientation, hence there is no basis for expecting strain in methyleoffyeloherane or cyclohexanone.
July 5, 1959
CONFORMATIONS AND STRAIN ENERGY OF CYCLOPENTANE
3217
The equilibrium conformations will be Cs for niethylcyclopentane and CZ for methylenecyclopentane. The values of (1 cos 3612) in Table I1 then yield for the difference in torsional strain
The strain free energy in the cyclopentane system is, therefore, 2.3 kcal./mole greater in the cyanohydrin than in the ketone. The calculations follow closely the method explained above for methylenecyclopentane and methylcyclopentane. One AEtmB = 0.25(3.40 - 2.80) f 1.70(2.80 - 1.98) readily calculates that the torsional strain energy = 1.54 kcal./mole of cyclopentanone is less than that of cyclopentane where the first term is the increase in torsional strain by 1.70(2.80 - 1.15) = 2.8 kcal./mole. The addiof methylcyclopentane over cyclopentane and the tional C-C-C bond angle strain in cyclopentanone second term the decrease of methylenecyclopentane must be very nearly the same as that in methylenecyclopentane, hence we take the same value of 0.9 below cyclopentane. The unstrained H-C-H bond angle in ethylene” kcal./mole. There do not appear to be any serious steric is larger than tetrahedral (117’) although the hindrance effects in the cyclopentanone cyanoforce constant is somewhat smaller (0.7 instead of 0.8 X lo-” erg/radian2). The ring angles were hydrin, but the torsional potential barriers are readjusted approximately to minimize the strain presumably somewhat greater than in cyclopentane. under these new conditions and the result indicated Barrowz0 gives 3.3 kcal./mole for the barrier to an increase in C-C-C bond angle strain of about methyl rotation in ethanol. The substitution of 0.9 kcal./mole in methylenecyclopentane above that the CN group might be expected to increase this value somewhat but we have no basis for an acin cyclopentane or in methylcyclopentane. The net result (1.54 - 0.9) is the calculated strain curate estimate. Fortunately the coefficient from energy difference of 0.61 kcal./mole which may be Table I1 for the Cs form is only 0.25, hence a crude compared to Turner and Garner’s experimental estimate will suffice. We take 4.0 kcal./mole for difference of 0.9 kcal./mole. This is as good the barrier adjacent to the C(0H)CN group and agreement as can be expected in view of the approxi- obtain 0.25(4.0 - 2.S) = 0.3 kcal./niole for the exmations made and the omission of differences in cess torsional strain over that of cyclopentane. Since the pseudo-rotation of the cyclopentane ring electron correlation energies. A somewhat similar argument may be applied is substantially restricted for both the ketone and to the data on the reaction of cyclic cyanohydrins the cyanohydrin, the entropy effects should apto form the cyclic ketone and hydrogen cyanide. proximately cancel and we find from the terms pre2.8 - 0.9 = 1.2 kcal./ Prelog and Kobelt’* report the standard free energy viously discussed 0.3 of dissociation to he 2.4 and 4.2 kcal./mole, re- mole for the excess strain in the cyanohydrin over spectively, for the cyclopentane and cyclohexane that of the ketone. The agreement of this figure The difference with the experimental value to 0.1 kcal./mole is, of systems in 9GyO alcohol a t 22-23’. of 1.8 kcal.,/mole may be attributed to the ap- course, fortuitous, since the calculation could easily err by 0.5 kcal./mole. Nevertheless, the propriate difference in strain free energies. Cyclohexanone is unstrained. The correspond- results indicate that the important effects are adeing cyanohydrin may have either the OH or the quately considered in these simple calculations. z 1 Fused rings offer a wide variety of situations; CN group axial with the other in the equatorial position. Various investigations of c y c l o h e ~ a n o l ~only ~ one will be mentioned here in concluding this indicate that the strain free energy of an axial discussion. The hydrindanes were considered by OH group is 0.G =t 0.2 kcal./niole. Such knowl- Dauben and Pitzerz2who emphasized the effects on edge as we have of the van der Waals repulsive the six-membered ring. We may now add that the contour of the CN group indicates that it will be ring fusion will also restrict the conformation of the less hindered in the axial position than the OH five-membered ring. Since the shared C-C bond is staggered (8 = 60’) in the normal chair conforgroup. At this point we must note that it is strain free mation of cyclohexane, the five-membered ring will energy which we are estimating for the cyanohydrin, tend to place its most nearly staggered bond in whereas it was strain energies (or enthalpies) in that location. Table I1 shows that this is bond earlier examples. If the cyanohydrin were purely 3 4 in the C2 conformation. Thus the fivea-CN, e-OH and the a-CN were strain free, there membered ring in hydrindane will take the Cz would still be a strain free energy of RT In 2 (or conformation with the unique CH:, group (1 in 0.4 kcal./mole a t 30O0\K.)because the elimination Fig. 2 ) in the 8-position. We note, however, from of the e-CN, a-OH conformation has reduced the Table I1 that 612 = 061 for the Cs conformation is entropy. In this case the 0.6 kcal./mole strain of only 2’ less than 834 in CZ. The difference in energy a-OH will not eliminate the a-OH conformation; ( 2 0 ) G. M. Barrow, J . Chem. P h y s . , 2 0 , 1739 (1952). (21) T h e heat of hydrogenation values for t h e cyclic ketones also the a-CN conformation may have a few tenths may also be discussed in a similar fashion. Unfortunately t h e kcal. strain. Hence an exact calculation is not large difference in heat of hydrogenation of cyclohexanone ( - 16.42) possible but the estimate of 0.5 + 0.2 kcal./mole for from those of acetone (-13.41) and methyl ethyl ketone (-13.19) the strain free energy of the cyclohexanone cyano- remains unexplained. T h e value for cyclopentanone is calculated t o be about 2.0 kcal./mole smaller t h a n t h a t of a n unstrained ketone, hydrin seems reliable.
+
+
(17) 1,. S. Bartell and R. A . Bonham, J . Chem. Phyr., $7, 1414 (10.57); H. C. Allen a n d E. K . Plyler, THISJ O U R N A L , 80, 2673 (1958). (18) V. Prelog and M. Kobelt, H e h . Chim. A d a , 3.2, 1187 (1949). (19) E. I
